# On Newton's First Law of Motion

This question is probably really stupid but I have to ask.

I take a pot of water and stir it. This creates a vortex. When I stop stirring, the water continues spinning before slowing to a stop. But Newton's First Law says that "Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed" and I thought that when I stop applying a force it should stop spinning since the water molecules would be accelerating in circular motion. There is another related issue. I decided to spin a trolley around and when I let go it kept spinning around. Why? (I know I'm probably missing something)

ZapperZ
Staff Emeritus
Conservation of angular momentum, the same way you have conservation of linear momentum.

Zz.

Right. But doesn't that violate Newton's First Law?

ZapperZ
Staff Emeritus
Right. But doesn't that violate Newton's First Law?
Why should it? A conservation of linear momentum (i.e. an object that continues to move in a straight line continues to move along that line after you stop pushing) doesn't violate the first law.

Consider this as a "rigid body" in which it is attached to something. It when you stop "torquing", the angular velocity is still there, but because it is confined by some central force, it will instead make a rotation.

Now, if it starts rotating FASTER, then that's a different matter.

Zz.

Newton's first law doesn't apply because there are forces still acting- the spinning trolley is a rigid body so the molecules at the edges have a net force acting on them towards the axis of rotation, due to their chemical bond with adjacent inner molecules.

Why should it? A conservation of linear momentum (i.e. an object that continues to move in a straight line continues to move along that line after you stop pushing) doesn't violate the first law.

Consider this as a "rigid body" in which it is attached to something. It when you stop "torquing", the angular velocity is still there, but because it is confined by some central force, it will instead make a rotation.

Now, if it starts rotating FASTER, then that's a different matter.

Zz.
So you're saying that the water continues to spin until it loses energy due to friction because when I stop applying the torque it is confined by the pot and could not move in a straight line. Or are you suggesting that an object remains in circular motion in the absence of a net torque?

Newton's first law doesn't apply because there are forces still acting- the spinning trolley is a rigid body so the molecules at the edges have a net force acting on them towards the axis of rotation, due to their chemical bond with adjacent inner molecules.

Newton's first law describes the motion of a single particle. If there is no force on that particle (part 1), then it will not accelerate (part 2).

You're correctly thinking that because a trolley is spinning, the atoms in the metal are accelerating towards the centre - applying part 2 of the principle to the individual atoms. However you're saying that the trolley has no net force on it - applying part 1 of the principle to the trolley as a whole.

You need to specify exactly what you are applying the law to first, and it will make sense.

There is no net force on the trolley as a whole, and the centre of mass of the trolley therefore does not accelerate. However there is a net force on individual atoms because the trolley is a rigid body (= the atoms MUST maintain their arrangement so moving one will mean the rest move, giving an internal force), so the outer atoms do accelerate towards the axis at the centre.

I imagine this is the solution to the first problem (I glanced at it) - try to be very specific as to what exactly you are applying the law to - the fluid as a whole? The individual molecules? This will force you to be consistent and you should not have any problems.

There is no net force on the trolley as a whole, and the centre of mass of the trolley therefore does not accelerate. However there is a net force on individual atoms because the trolley is a rigid body (= the atoms MUST maintain their arrangement so moving one will mean the rest move, giving an internal force), so the outer atoms do accelerate towards the axis at the centre.
Maybe it's because of the lateness of the night but I only partially understand. You said that moving one atom will cause the others to move because the trolley is a rigid body. But when did I move this atom? Thanks.

This is not happening here, it was just an example to illustrate how a body can have internal forces without external forces.

Consider a barbell spinning in empty space. There is no net force on the barbell as a whole. However, there is a tension in the handle to maintain the rigidity of the barbell, because the handle must exert a force on each end to keep them in circular motion.

Simply put,

Apply N1 to particles: force on particle = internal force which is nonzero = particle accelerates towards centre causing circular motion
Apply N1 to trolley : force on trolley = external force which is zero = trolley centre of mass does not accelerate.